The Rotherham-born politician makes the prediction in her monthly column for The Yorkshire Post in which she urges Tory colleagues to come up with new ideas to transform the country.
Her intervention comes after the Prime Minister met senior Tory backbenchers to discuss the date of her departure from 10 Downing Street.
“We’re about to embark on a brand-new aspect of broken politics – a Tory leadership campaign, with more runners and riders than you see at Doncaster Races. So at a time of national crisis, rather than putting all its time into dealing with that, my party is about to prioritise a conversation with itself,” writes Ms Greening who served as Education Secretary until January last year.
“A typical contest will see candidates focus on winning over the 150,000 people in the Conservative ‘tribe’ first and worry about everyone else later. But there’s nothing typical about the times we live in, so on this occasion, that’s surely the wrong way around.
“All it will deliver is a Pyrrhic victory, because any new Prime Minster will face the same Parliamentary maths and the same Brexit gridlock.”
Reiterating her call for a second referendum, the leading Remain supporter wants a renewed focus on social mobility. “My vision is a country where no matter who or what you are, or where you start, you can go as far as your talents can take you,” she adds.
“Driving strong social mobility needs a level of radical thinking and ambition well beyond anything we’ve seen before. And action now, not just promises of change tomorrow. A strategy that can galvanise a whole country.”